Design of fault-tolerant networks for satellites (TWTA redundancy)

This article deals with the design of networks to be loaded on satellites. These networks should connect inputs (corresponding to signals arriving on the satellite) to outputs (corresponding to ampli ers), even in case of failures of ampli ers. They are made of links and expensive switches, hence we want to minimise the number of switches subject to the following conditions: each input and each output is connected to exactly one switch; each switch is adjacent to exactly four links; there are n inputs and n+ k outputs; among the n + k outputs, k can fail permanently and nally all the input signals should be sent to valid ampli ers, (outputs), via disjoint paths. So, the aim is to design networks having as few switches as possible and satisfying the following property: there exist n edge-disjoint paths from the n inputs to any set of n outputs chosen from the n + k total number of outputs. We call such networks valid k-fault tolerant networks. Let N (n; k) denote the minimum number of switches of a valid network with n inputs, n+ k outputs and k output failures. In this article, we give some details on the problem, and some preliminary results such as the fact that N (n; k) n. We also propose a general construction which yields (under some conditions) N (n + n0; k) N (n; k) +N (n0; k).